The crime rates in other places is irrelevant if the city you've lived in for the last 20 years has become noticeably more dangerous.
This is not "a narrative that keeps being pushed without merit", in fact the people who dismiss such claims are often the ones who live very insulated lives.
I've been here 25 years, and most of the areas that used to be sketchy are now not.
I witnessed the aftermath of a murder last week in Stoke Newington! (Saw that the road had been closed off)
I've seen women publicly urinating into drains on a busy road (Hackney)
There are massive increases in the number of homeless people (Tooting, Clapton, Shadwell), several times I've seen a homeless looking person harass women passing by.
Seen needles lying around (Shadwell, Commercial Road)
The general advice now is never to wear a watch in Central London, this wasn't the case 10 years ago.
I've seen security guards restrain people trying to leave shops in Central London after they shoplifted.
So yeah, some areas might not look sketchy, and these gentrified places (e.g. Stoke Newington) might be ok if you stick to the bars, restaurants and then Uber home, but for a lot of people these remain dangerous if you're in the wrong place at the wrong time.